Alonzo Church sees in Frege's thinking that the reference of a sentence
is that sentence's truth-value an exoneration of the idea that if
sentences designate propositions then all designate the very same
proposition. Church demonstrates this by providing a slingshot argument
in his 1943 review of Carnap's 'Introduction to Semantics' and he also
reiterates it in his 1956 'Introduction to Mathematical Logic'. Indeed,
Frege does not *use* any slingshot argument.
Around the same time that Church's review of Carnap appeared, Goedel
wrote "Russell's Mathematical Logic" (1944), footnote 5 of which has a
proof sketch for the Fregean conclusion that all true propositions have
the same signification. {Goedel uses a much weaker principle than
logical equivalence, one according to which "Fa" and "a = ix((x = a) &
Fx)" have 'the same meaning'). Neale's 1995 Mind paper (and the 2001
book 'Facing Facts' that grew out of that paper) is very good on all
this.
The received wisdom in combating the slingshot argument is that we need
to undermine the referential status of definite descriptions and this is
aptly done by understanding Russell's reasons for thinking that definite
descriptions as syncategorematic terms. But, if we rearticulate the
slingshot argument in terms of set abstracts (taken as primitive, as
Heck suggests, so definite descriptions are definable in terms of these)
then the issue of the semantics of definite descriptions becomes an
irrelevant one. I suspect Goedel appreciated this very point. In
discussing the Russellian escape route (in the 1944 paper referred to
above) he says:
"I cannot help feeling that the problem raised by Frege's puzzling
conclusion [that all true sentences have the same signification]
has
only been evaded by Russell's theory of descriptions and that there
is
something behind it which is not yet completely understood. "
(page 215 in the 1964 edition of the Benacerraf and Putnam anthology
on
Philosophy of Mathematics)
Part of what was not "completely understood" then (I humbly suggest) is
the fact that set abstractions do the very job iota-expressions are
supposed to do without raising these semantic issues and, thus,
solidifying the slingshot argument.
Arhat Virdi